document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949625>Question 949625</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to solve this problem:\r<BR>\n" );
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document.write( "Mark takes out a loan of 40,000 that is must be repaid over the course of 5 years. Interest is compounded at a nominal rate of 9% convertible monthly and he makes 60 scheduled repayments of 735 at the end of each month. What additional payment must he make at the end of the term so that the loan is completely paid off? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579852 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=579852\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%229%25%22=9%2F100=0.09 ALIGN=MIDDLE  ALT=\"%229%25%22=9%2F100=0.09\"   DISABLED_style= \"max-width:90%; height:auto;\" > nominal rate convertible monthly means that<BR>\n" );
document.write( "each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the year (1 month) they add  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%229%25%22 ALIGN=MIDDLE  ALT=\"%229%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F12%29%2A0.09=0.0075 ALIGN=MIDDLE  ALT=\"%281%2F12%29%2A0.09=0.0075\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the old balance,<BR>\n" );
document.write( "to the old balance to calculate the new balance.<BR>\n" );
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document.write( "At the end of the first month, just as Mark is about to make his first payment,<BR>\n" );
document.write( "they add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0075%2A%28%22%2440%2C000%22%29 ALIGN=MIDDLE  ALT=\"0.0075%2A%28%22%2440%2C000%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2440%2C000%22 ALIGN=MIDDLE  ALT=\"%22%2440%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2440%2C000%22%2B0.0075%2A%28%22%2440%2C000%22%29=%281%2B0.0075%29%2A%28%22%2440%2C000%22%29=1.0075%2A%28%22%2440%2C000%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075 ALIGN=MIDDLE  ALT=\"1.0075\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the previous balance.<BR>\n" );
document.write( "Immediately, Mark makes his <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%24735%22 ALIGN=MIDDLE  ALT=\"%22%24735%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > payment, and the balance goes down to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075%2A%28%22%2440%2C000%22%29-%22%24735%22 ALIGN=MIDDLE  ALT=\"1.0075%2A%28%22%2440%2C000%22%29-%22%24735%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "At the end of the second month, just as Mark is about to make his second payment,<BR>\n" );
document.write( "the balance again increases by a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075 ALIGN=MIDDLE  ALT=\"1.0075\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075%2A%28%22%2440%2C000%22%29-%22%24735%22 ALIGN=MIDDLE  ALT=\"1.0075%2A%28%22%2440%2C000%22%29-%22%24735%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075%5E2%2A%28%22%2440%2C000%22%29-%22%24735%22%2A1.0075 ALIGN=MIDDLE  ALT=\"1.0075%5E2%2A%28%22%2440%2C000%22%29-%22%24735%22%2A1.0075\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "only to get immediately reduced by the second <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%24735%22 ALIGN=MIDDLE  ALT=\"%22%24735%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > payment<BR>\n" );
document.write( "to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075%5E2%2A%28%22%2440%2C000%22%29-%22%24735%22%2A1.0075-%22%24735%22 ALIGN=MIDDLE  ALT=\"1.0075%5E2%2A%28%22%2440%2C000%22%29-%22%24735%22%2A1.0075-%22%24735%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "At the end of the second month,<BR>\n" );
document.write( "the balance first increases again by a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075 ALIGN=MIDDLE  ALT=\"1.0075\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075%5E3%2A%28%22%2440%2C000%22%29-%22%24735%22%2A1.0075%5E2-%22%24735%22%2A1.0075 ALIGN=MIDDLE  ALT=\"1.0075%5E3%2A%28%22%2440%2C000%22%29-%22%24735%22%2A1.0075%5E2-%22%24735%22%2A1.0075\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and then<BR>\n" );
document.write( "decreases to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075%5E3%2A%28%22%2440%2C000%22%29-%22%24735%22%2A1.0075%5E2-%22%24735%22%2A1.0075-%22%24735%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "with the third <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%24735%22 ALIGN=MIDDLE  ALT=\"%22%24735%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > payment.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The pattern repeats each month, so after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2A5=60 ALIGN=MIDDLE  ALT=\"12%2A5=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > months, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" > payments, the balance is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075%5E60%2A%28%22%2440%2C000%22%29-%22%24735%22%2A1.0075%5E59-%22%24735%22%2A1.0075%5E58-%22...%22-%22%24735%22%2A1.0075%5E2-%22%24735%22%2A1.0075-%22%24735%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075%5E60%2A%28%22%2440%2C000%22%29-%22%24735%22%2A%281.0075%5E59%2B1.0075%5E58%2B%22...%22%2B1.0075%5E2%2B1.0075%2B1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From either geometric sequences and series,<BR>\n" );
document.write( "or from polynomial s and factoring, we know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075%5E59%2B1.0075%5E58%2B%22...%22%2B1.0075%5E2%2B1.0075%2B1=%281.0075%5E60-1%29%2F%281.0075-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So the final balance, after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" > months, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" > payments is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.0075%5E60%2A%28%22%2440%2C000%22%29-%22%24735%22%2A%281.0075%5E60-1%29%2F%281.0075-1%29=highlight%28%22%247%2C190.50%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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